New theories are hard to get right…but that’s OK

Albert Einstein in Pittsburgh, 1934. Note that the blackboard is covered with equations of relativity, which are its most accurate expression. [Credit: Pittsburgh Sun-Telegraph/Dwight Vincent and David Topper]

I get at least one email each week asking me to read and comment on a new proposed theory, usually having to do with overthrowing the Big Bang theory, refuting Einstein (mostly by contradicting relativity), or replacing dark matter with a new concept. Many of these ideas are quite sophisticated (while others um…are distinctly not), but they share a lot of characteristics:

The authors are often intelligent people, frequently skilled professionals in various fields (especially engineering for some reason). They possess a lot of knowledge, but have little or no formal physics training.

The theories are presented as logical arguments, sometimes with diagrams, but few or no equations.

Similarly, the proposed theories make general sweeping predictions, but few propose specific experiments or observations that would provide a way to test them. (They do often contain thought experiments, about which I’ll have more to say presently.)

The authors express a strong sense of frustration that nobody in the establishment will listen to their theories, even while they rarely cite published previously published work in the field. The exception is usually popular science writing or TV shows. The people writing to me are often widely-read and conversant with the popular accounts of string theory, cosmology, relativity, and other topics in theoretical physics.

(Another common factor that is sociologically interesting but not relevant to today’s post: nearly all of these writers are white males.)

I get that the world of physics can seem daunting. There are real obstacles to people who want to become physicists, both systemic and inherent. The systemic barriers come down to access to education and related issues (e.g. family support), a topic I am passionate about, but which is far beyond my primitive means to address. The inherent obstacles, though, can be summed up very simply.

Theoretical physics is hard.

Or more to the point: coming up with workable new theories in physics is difficult. Partly that’s because of the vast successes of science: we are remarkably good with our current theories at describing, predicting, and otherwise characterizing a huge number of physical phenomena. Any new theory has to cover known phenomena adequately and do better at characterizing experimental or observational evidence than existing successful models. That’s hard to do, which is why big shifts in the way we do things — relativity, quantum physics, and so forth — are much rarer than smaller advances.

Sometimes I wonder if popular science writing of the kind I do can be a disservice to some people. After all, one of my missions is to help non-specialists understand some of the complex ideas underlying modern physics. However, it’s much harder to learn how to do the calculations yourself, which is a crucial part of being an actual theoretical physicist. I want to show you why physics works, and a bit of the mechanism of how it works, but the limits of the medium — and of most readers’ interests and time — I can’t show you very well how to do it yourself.

You can appreciate the music of Bach without playing piano, but most of us will never be able to perform the Well-Tempered Clavier without some kind of instruction, or at least many hours of hard work at the keyboard. Physics is no different: you may understand the concepts behind relativity pretty well (if writers like me are doing our jobs!), but that’s not sufficient to do relativity calculations yourself. And unless you know how to do the calculations, you’re going to have a very hard time coming up with an alternative theory that describes the same phenomena that physicists and astronomers have been measuring for over a century.

Learning to be a physicist is also akin to an apprenticeship in a craft: you learn to be creative by seeing what has already been done and what works. Sometimes when you know the rules, you can break them: knowing the rules of classical geometry allowed Lobachevsky, Bolyai, Gauss, and others to find entirely new types of geometry, kinds we use in modern physics. To be a theoretical physicist today, you should know how relativity and quantum mechanics work on a fundamental level and why they are successful theories. When you have that knowledge, maybe you’ll find exceptions to their rules, but it’s unlikely you’ll succeed without a thorough grounding in standard physics first.

It’s all in your head

Another tricky aspect involves the role of thought experiments, which are both a staple of popular-science writing and used by working researchers. As the name suggests, instead of (or, for preference, in addition to) performing experiments in the lab, you work out what the results of an experiment should be virtually, using the principles of the theory under development. Einstein is probably the most famous thought experimenter: he used a number of them to help him with the trickier aspects of relativity, as well as to criticize some of the aspects of quantum physics he disliked. Thought experiments are really handy, especially in situations where a real experiment might be impractical (e.g., accelerating a spaceship close to the speed of light).

People who send me radical new ideas are very fond of thought experiments. However, thought experiments are beholden to both theory and real experiments. A scientific theory isn’t just a random thought, after all: it’s a coherent framework of testable hypotheses. It’s possible for a thought experiment to simply not make sense, making it useless from a scientific point of view; I’ve received a number of these that contradict known physical phenomena.

Sometimes reality just sucks

Once again, I get where purveyors of radical theories are coming from. There’s a lot about the Universe that can seem weird or even wrong. Dark matter is a prime example: I’m pretty sure most physicists and astronomers would be very happy if it just went away. After all, it’s invisible (making it hard to detect directly) and isn’t made of any of the components of normal matter (making it annoying). However, astronomical observations force us to accept its existence; any alternative idea has to explain all the same phenomena, and none have passed that test thus far. To put it another way, dark matter is the worst solution to the problem, except for all the other proposals.

Similarly, the Big Bang model seems to describe our Universe extremely well, strange as it is. Think of it this way: before cosmology became a branch of science, it was the purview of philosophy and religion. Many of those cosmologies postulated a cyclic cosmos, a small reality in which Earth was a significant portion, and/or an eternal existence of some form. All of these ideas appear inconsistent with the Universe we observe. We may yet end up with another model, but not one in which we occupy a special position; those days are gone forever.

Einstein famously disliked many aspects of quantum physics; while he has often been mocked for that, his criticisms were a lot more sophisticated than just “God doesn’t play dice”. (I would like a dollar for every time someone invokes that phrase out of its proper context, please.) He was wrong about many things, but he had his reasons — and he returned to physics to make his points. His example is illustrative: he was brilliant, contributed many things to physics, was right about many things, wrong about others — but ultimately isn’t the arbiter of how the Universe behaves.

Perhaps in the end, the most difficult act in science is accepting that the cosmos need not conform to our wishes. Scientific training is largely devoted to learning that, though we rarely put it that way. Theoretical physics is hard simply because we have to make it match reality, and reality doesn’t always cooperate. However, if you can get over that mental hurdle, you may find the real Universe is beautiful in itself, and contemplating it is one of the most glorious endeavors a human —physicist or not— can engage in.

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11 Responses to “New theories are hard to get right…but that’s OK”

Equations just depict ideas. Equations can be very hard. Some we have no …idea how to handle them (Navier-Stokes, a most useful equation).

It’s hard to find new ideas. However, some, once found and accepted, can be amazingly simple. The invention of Non-Euclidean geometry just amounted to admit a pre-Euclidean idea: one could make geometry on a sphere, or a saddle, not just a plane.

It was more of a philosophical change of perspective than anything else.

Similarly Einstein took Poincare’s observation that the constancy of the speed of light should be viewed as a physical law, and got the Lorentz group from it. Modulo some mathematics so trivial, Poincare’ had not bother to make them explicit.

Again a philosophical change of perspective.

Or Einstein (again) took Planck’s idea of quantified emission of light, and decided that was proof enough that there was such a thing as light quanta Planck disapproved, but that “explained” the photoelectric effect discovered 80 years earlier (Einstein got the Nobel for that simple idea in 1923).

Philosophical change of perspective, again.

The discovery of Dark Matter and Dark Energy were as unexpected as that of Quantum Theory. However the Quantum “explained” right away two well-known, yet baffling, experimental facts; the non-occurring “ultraviolet catastrophe”, and the Blackbody Radiation.

In the present situation, we are not even completely sure that Dark Matter and Dark Energy are really observed facts. The philosophical perspectives, let alone the physical ones, are vast. Breakthroughs will come, first, from simple ideas. Complicated equations will follow.

We appreciate the brutal beauty of the universe as our judge, because we evolved that way. To find those elements of reality we call the truth. Our glorious survival blossomed that way.

What you say sounds reasonable on its face, but there are number of problems with your arguments.

We use equations in physics because they are effective. The Navier-Stokes equation helps us describe physical phenomena successfully; it doesn’t matter whether you understand it philosophically or not. To cite the most important example of all: people still debate over the proper way to interpret quantum mechanics, but everyone uses the Schrödinger equation and the other mathematical tools because those are the way to do quantum physics. That’s not to say the interpretation isn’t important, but the equations are essential.

Also, you get the cosmological issues backward. Dark matter and dark energy are observed phenomena (“facts” if you will, though I dislike using that term). “Dark energy” in particular is just the name we give to the observed accelerated expansion of the Universe, for which we currently don’t have a good theoretical explanation. “Dark matter” similarly is the name we give to the simplest explanation for a wide variety of astronomical observations, from the rotation of galaxies to the sound waves in the cosmic microwave background (see the detailed discussion in https://galileospendulum.org/2013/03/21/planck-results-our-weird-and-wonderful-universe/ for more on that second point). These are observations for which we need more theory and observation, not philosophical perspectives.

Conceptual breakthroughs happen, but they follow hard work. Newton didn’t spontaneously come up with gravity, and Einstein didn’t spontaneously think of relativity. Both of these breakthroughs came after long strenuous efforts, and were built on ideas, experiments, and observations from many others who came before them. When we figure them out, dark energy and dark matter will be no different. After all, we’ve known about dark matter since the 1930s and dark energy since 1998 (with inklings of its existence before then). If all it took was a philosophical perspective, we’d have solved it by now.

Dear Matthew: I did not say the Navier-Stokes equation had to be understood “philosophically”. I just alluded to the fact that, although it depicts fluid flow, the general existence and smoothness solutions of this non linear PDE have not been proven (I actually don’t believe they exist).

Newton did not come up with the gravity law, by the way. He exploited it further.

The French astronomer Ismaël Boulliau suggested that Kepler was wrong about the gravitational force. Kepler had declared that the gravitational force holding the planets in place decreased inversely to distance. Boulliau held instead that the force decreased as an inverse square law. He deduced this in analogy to light. Isaac Newton acknowledged Boulliau’s discovery.

Nobody dares to suggest the equations related to Quantum Theory are not essential. To a great extent, they are all what defines the theory. QFT is all about guessing the Laplacian, aka the equation(s).

The situation with Dark Stuff is not similar. They are not directly observed phenomena (just ask LHC people).

The “observations” of both Dark Matter and Dark Energy are the fruits of (philosophical) pruning. The former depends, among other things, upon the hypothesis that gravity holds at galactic scales (some employed astronomers claim gravity does not work beyond the Solar System… as seems to be the case, at face value!) It’s hard to evaluate things we don’t know, such as galactic mass (the Milky Way has grown in astronomers’ minds recently) to make further guesses about something else.

In the case of Super Novae studies, outliers explosions are removed from the sampling. I could not read a clear enough description of what was found (I read the original literature) to see if my pet theory survives.

Boldly supposing that something is really going on (I know a Nobel was attributed), we are very far from being able to describe the thing (whether, for example it’s a Cosmological Constant or Quintessence field description).

Physics is what we do, it did not start with Newton. Or Buridan, who discovered inertia, or Aristotle, who got that wrong.

Also, please review my comment policy (), especially item 3: “…the comments are not a space for you to expound on your own theories, promote your own ideas, or tout conspiracy theories. I reserve the right to edit or delete comments of that sort summarily. You can start your own blog and write whatever you want there (within limits, of course), but you don’t have the right to expect me to provide free advertising space for you. If you feel the need to compare yourself to Copernicus, Einstein, or Galileo, then you’re probably going to find yourself edited or deleted.”

Math is independent of discovery. Erasto Mpemba was making ice cream. Should math overall exclude external observation? General Buck Turgidson, “Well, I, uh, don’t think it’s quite fair to condemn a whole program because of a single slip-up, sir.” Dr. Strangelove The “single slip-up” sent 1400 megatons to bomb the USSR.

BTW, I did not expound theory. I described an experiment that challenged prevailing maths for being non-physical by observation. Empirical failure falsifies postulates not derivations (Euclid’s fifth postulate and cartography).